Bourbaki

Example 1

Tag 06EY, permanent. Cite it as [Bourbaki, Tag 06EY].

Algebra, chapter IV, § 6. Symmetric functions

Given Λ,μ\Lambda, \mu in Λ\Lambda, we have the formulae

res⁡p,0(f,λ)=λp,res⁡0,q(μ,g)=μq \operatorname{res}_{p,0}(f, \lambda) = \lambda^p, \quad \operatorname{res}_{0,q}(\mu, g) = \mu^q
res⁡p,1(f,λ)=λptp,res⁡1,q(μ,g)=(−1)qμquq, \operatorname{res}_{p,1}(f, \lambda) = \lambda^p t_p, \quad \operatorname{res}_{1,q}(\mu, g) = (-1)^q \mu^q u_q,
whose proof is immediate.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

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Cites

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Transcribed from the printed edition, 2003, Springer. Not translated.